All of signal processing went from, "We'd like to do a Fourier Transform but can't afford O(n^2) so here is a faster alternative that kind of does something useful" to, "We start with a FFT."
Neural nets opened a lot of doors.
Bellman equation is in a lot of equipment.
Also I don't really think taking a Taylor series for the inverse square root should count as an "algorithm."
That's what ID Software thought:
http://en.wikipedia.org/wiki/Fast_inverse_square_root#Overvi...
Deep belief nets have made things that look like neural nets popular again, but things like sparse ICA stacks is suggestive of another wave of theory led morphing back to non-neural architecture. But the point is that the theory followed after the invention of neural architectures both times. So the root is the ANN, and thus I think it is a really important algorithm in history. It was a bio inspired innovation too which is interesting.